Any of those flight websites are fine, but be cautious if they suggest that you buy your tickets from a website other than an airline. There can be some complications if you buy from someone like Vayama and you run into a flight delay or cancellation.
It's too early to buy tickets for April 2019, but it's very helpful to monitor prices for your desired destination for a good while before clicking the "Buy" button. That way, you'll have a good sense of what the normal price range is. Fares move up and down a lot on some routes. If you have a sense of "normal" you'll recognize an odd fare spike when you see one, and you won't buy then (or you'll look for an alternative set of flights that's almost as good and hasn't spiked upward). Similarly, if you have a good idea of the typical pricing and one day the fare is $200 lower, you'll know you are looking at a good deal.
I sort of doubt that you will find significant-enough price differences to make it worthwhile to fly out of one of the NYC-area airports (what will it cost you to get there or to park your car for the duration of the trip? And how much extra time will you need to allow for that trip north, to be 100% certain you don't miss the flight? Still, I would certainly check fares from Newark and JFK. At some level of savings it becomes worthwhile to travel a little farther.
You'll probably be able to get a good deal on a flight to Rome in April next year. Easter falls on April 21, and there could be some holiday impact on fares around that time, so if you can be a bit flexible on your travel dates, that may prove to be beneficial.
Most trips, especially to Italy--a long, skinny country--benefit from purchase of what is called a "multi-city" ticket. That allows you to fly into one city and out of another. One should always compare the multi-city price to a roundtrip to the cheapest practical destination in Italy (from where I live, that would be Rome or Milan, but from Philly, it might be different). If you fly in and out of the same city in Italy, you will almost certainly spend several hours on trains getting back to your starting point, and that will cost some money as well as precious vacation time.